# Simplifying numerical solution of constrained PDE systems through involutive completion

Bijan Mohammadi; Jukka Tuomela

- Volume: 39, Issue: 5, page 909-929
- ISSN: 0764-583X

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topMohammadi, Bijan, and Tuomela, Jukka. "Simplifying numerical solution of constrained PDE systems through involutive completion." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 39.5 (2005): 909-929. <http://eudml.org/doc/244671>.

@article{Mohammadi2005,

abstract = {When analysing general systems of PDEs, it is important first to find the involutive form of the initial system. This is because the properties of the system cannot in general be determined if the system is not involutive. We show that the notion of involutivity is also interesting from the numerical point of view. The use of the involutive form of the system allows one to consider quite general situations in a unified way. We illustrate our approach on the numerical solution of several flow equations with the aim of showing the impact of the involutive form of the systems in simplifying numerical schemes.},

author = {Mohammadi, Bijan, Tuomela, Jukka},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {overdetermined PDEs; involution; discretization; elliptic systems; involutive form; overdetermined systems; auxiliary variables},

language = {eng},

number = {5},

pages = {909-929},

publisher = {EDP-Sciences},

title = {Simplifying numerical solution of constrained PDE systems through involutive completion},

url = {http://eudml.org/doc/244671},

volume = {39},

year = {2005},

}

TY - JOUR

AU - Mohammadi, Bijan

AU - Tuomela, Jukka

TI - Simplifying numerical solution of constrained PDE systems through involutive completion

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2005

PB - EDP-Sciences

VL - 39

IS - 5

SP - 909

EP - 929

AB - When analysing general systems of PDEs, it is important first to find the involutive form of the initial system. This is because the properties of the system cannot in general be determined if the system is not involutive. We show that the notion of involutivity is also interesting from the numerical point of view. The use of the involutive form of the system allows one to consider quite general situations in a unified way. We illustrate our approach on the numerical solution of several flow equations with the aim of showing the impact of the involutive form of the systems in simplifying numerical schemes.

LA - eng

KW - overdetermined PDEs; involution; discretization; elliptic systems; involutive form; overdetermined systems; auxiliary variables

UR - http://eudml.org/doc/244671

ER -

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